Re: Happy 2013

Yes, and I just got a message from one of the authors on the explanation:

"2013 is the smallest number that needs at least six squares to make."

That means that 2013 is the smallest number that *requires* at least six squares to produce. Yes, there are smaller numbers that can be made with six squares. But all of those numbers can also be made with five or fewer squares

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.In biology, we use math like we know what we are talking about. Sad isn't it.

Re: Happy 2013

I believe so. Otherwise, I suppose there's a way to stuff in a bunch of small 2^2's and 3^2's to fill in the gaps... Can't use any 2^1's though... I believe that's cheat'n

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.In biology, we use math like we know what we are talking about. Sad isn't it.

Re: Happy 2013

Found it! Seems like 2013 = 47^2-19^2+13^2-2^2So it can be made up by only 4 prime squares! Cool!

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.In biology, we use math like we know what we are talking about. Sad isn't it.

Re: Happy 2013

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Re: Happy 2013

It does. Try to look at the bottom

This one is a little more abstruse. Imagine a game whereby you make numbers by adding or subtracting squares of prime numbers. E.g., 30 = (5 x 5) + (3 x 3)  (2 x 2). 2013 is the smallest number that needs at least six squares to make. (Can you figure them out?)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Re: Happy 2013

True, it might be erroneous but it's worth claiming just for the inspiration!

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.In biology, we use math like we know what we are talking about. Sad isn't it.

Re: Happy 2013

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.In biology, we use math like we know what we are talking about. Sad isn't it.

Re: Happy 2013

Interesting that 2013 is composed of four sequential digits: 0, 1, 2 and 3. That hasn't happened since 1432... 581 years ago!

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.In biology, we use math like we know what we are talking about. Sad isn't it.

Re: Happy 2013

Also interesting is that 2013 to 2015 are consecutive numbers each with unique factors. That happened last in 1885-1887 and happens again in 2665-2667.

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.In biology, we use math like we know what we are talking about. Sad isn't it.

Re: Happy 2013

Hi pellerinb!

I don't understand what you mean y "each with unique factors" for the consecutive numbers(necessarily odd since if even they would have 2 in common). Any two consecutive odd integersmust have no factors in common other than 1 since the difference of the two (larger less smaller)is 2. This means the only possible common factors are 2 and 1 and certainly 2 is not a commonfactor for these odd integers.

Please clarify.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

Re: Happy 2013

Sorry about that. Each triple (2013 to 2015, 1885 to 1887 and 2665 to 2667) has numbers with exactly three distinct prime factors each.

Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.In biology, we use math like we know what we are talking about. Sad isn't it.

Re: Happy 2013

@Bob bundy,

Hasn't a few months passed already?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Re: Happy 2013

Very Well

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.''God exists because Mathematics is consistent, and the devil exists because we cannot prove it''But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Re: Happy 2013

Happy Fibonacci day. Just a hundred years to the next one!

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.